  # scipy stats.foldcauchy () | python

NumPy | Python Methods and Functions

scipy.stats.foldcauchy () is a folded continuous Cauchy random variable that is defined in a standard format and with some shape parameters to complete its specification.

Parameters:
- & gt; q: lower and upper tail probability
- & gt; a: shape parameters
- & gt; x: quantiles
- & gt; loc: [optional] location parameter. Default = 0
- & gt; scale: [optional] scale parameter. Default = 1
- & gt; size: [tuple of ints, optional] shape or random variates.
- & gt; moments: [optional] composed of letters [`mvsk`]; `m` = mean, `v` = variance, `s` = Fisher`s skew and `k` = Fisher`s kurtosis. (default = `mv`).

Results: folded Cauchy continuous random variable

Code # 1: Create a folded Cauchy continuous random variable Cauchy random variable

 ` from ` ` scipy.stats ` ` import ` ` foldcauchy ` ` `  ` numargs ` ` = ` ` foldcauchy.numargs ` ` [a] ` ` = ` ` [` ` 0.7 ` `,] ` ` * ` ` numargs ` ` rv ` ` = ` ` foldcauchy (a) `   < p> ` print ` ` (` ` "RV:" ` `, rv) `

Exit:

` RV: & lt; scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D55D8E160 & gt; `

Code # 2: the folded Cauchy random variables and the probability distribution function.

` `

 ` import ` ` numpy as np ` ` quantile ` ` = ` ` np.arange (` ` 0.01 ` `, ` ` 1 ` `, ` ` 0.1 ` `) `   ` # Random Variants ` ` R = foldcauchy.rvs (a, scale = 2 , size = 10 ) `` print ( "Random Variates:" , R)   # PDF R = foldcauchy.pdf (a, quantile, loc = 0 , scale = 1 ) print ( "Probability Distribution:" , R)  `

Output:

` Random Variates: [1.7445128 2.82630984 0.81871044 5.19668279 7.81537565 1.67855736 3.35417067 0.13838753 1.29145462 1.90601065] Probability Distribution: [0.42727064 0.42832192 0.43080143 0.43385803 0.43622229 0.43639823 0.4 3294602 0.42480391 0.41154712 0.3934792] `

Code # 3: Graphic representation.

` `

 ` import ` ` numpy as np ` ` import ` ` matplotlib.pyplot as plt ``   distribution = np.linspace ( 0 , np.minimum (rv.dist. b, 3 )) print ( "Distribution:" , distribution)   plot = plt.plot (distributio n, rv.pdf (distribution)) `

Output:

` Distribution: [0. 0.06122449 0.12244898 0.18367347 0.24489796 0.30612245 0.36734694 0.42857143 0.48979592 0.55102041 0.6122449 0.67346939 0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633 1.10204082 1.16326531 1.2244898 1.28571429 1.34693878 1.40816327 1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102 1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714 2.20408163 2.26530612 2.32653061 2.3877551 2.44897959 2.51020408 2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102 2.93877551 3. ] `

Code # 4: Various Positional Arguments

 ` import ` ` matplotlib. pyplot as plt ` ` import ` numpy as np   ` x ` ` = ` ` np.linspace (` ` 0 ` `, ` ` 5 ` `, ` ` 100 ` `) `   ` # Various positional arguments ` ` y1 ` ` = ` ` foldcauchy.pdf (x, 1 , 3 ) `` y2 = foldcauchy.pdf (x, 1 , 4 ) plt.plot (x, y1, "*" , x, y2, "r--" ) `

Output: